I don't think cops will write a ticket for parking on private property especially since my argument would be that unless they have a sign saying "No overnight parking", then permission to park is implied.
In any event I have found it is usually better to apologize after the fact than asking permission in advance because often times you go undetected so no apology needed.
While I do agree it's often better to ask forgiveness as anachronism pointed out your reasoning is not true and in my experience resort towns often aggressively discourage it otherwise they would have all kinds of ski bums and what not sleeping in cars all over town. The normal type of tourist would be intimidated or put off by such an image. The town makes a lot more money of off people that are willing to pay for hotels than the guy who would rather sleep in the front seat of his subaru than pay for hotel so they care more about the former's opinion. They could care less if the car camper never comes back after paying his fine.